The rapid development of the theories of Volterra integral and functional equations has been strongly promoted by their applications in physics, engineering and biology. This text shows that the theory of Volterra equations exhibits a rich variety of features t present in the theory of ordinary differential equations. The book is divided into three parts. The first considers linear theory and the second deals with quasilinear equations and existence problems for nlinear equations, giving some general asymptotic results. Part III is devoted to frequency domain methods in the study of nlinear equations. The entire text analyses n-dimensional rather than scalar equations, giving greater generality and wider applicability and facilitating generalisations to infinite-dimensional spaces. The book is generally self contained and assumes only a basic kwledge of analysis. The many exercises illustrate the development of the theory and its applications, making this book accessible to researchers in all areas of integral and differential equations.